Our construction generalizes a construction from [1]} which is specialized for \(a=1\)  and requires a field size of \(n^{h-\lceil h/g\rceil +1}\) . Our construction analyses this generalization with a new and direct proof using simple linear algebra and basic properties of Vandermonde matrices and Gabidulin codes. Our construction and its proof is inspired by the constructions of MR LRCs in [2]}, [3]}.
